The Vander Waal’s equation for a gas is $(p + \frac{a}{v^{2}}) (V - b) = n R T$ where p, V, R T and n represent the pressure, volume, universal gas constant absolute temperature and number of moles of a gas respectively, a and b are constants. The ratio b/a will have the following dimensional formula

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MLT^-2

M^-1 L^-2T²

M^-1 L^-1T¹

ML²T²

answer is A.

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Detailed Solution

According to principle of homogeneity all the terms of a given equation have same units and dimensions. Quantities having the same units and dimension can be added or subtracted b will have the dimensions of volume

$\frac{a}{V^{2}}$ will have dimensions of pressure

$\frac{a}{V^{2}} = P$ and $b = V$

$\begin{array}{l} \frac{b}{a} = \frac{V}{P V^{2}} \\ = \frac{1}{P V} \\ = \frac{1}{w o r k d o n e} \\ = \frac{1}{M L^{2} T^{- 2}} \\ = M^{- 1} L^{- 2} T^{2} \end{array}$